<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Lists and Tables</title> <link rel="stylesheet" href="../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.75.2"> <link rel="home" href="../index.html" title="Document To Test Formatting"> <link rel="up" href="../index.html" title="Document To Test Formatting"> <link rel="prev" href="blurbs.html" title="Blurbs"> <link rel="next" href="images.html" title="Images"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td> <td align="center"><a href="../../../../index.html">Home</a></td> <td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td 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href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.lists">Lists</a></span></dt> <dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.variable_lists">Variable Lists</a></span></dt> <dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.tables">Tables</a></span></dt> </dl></div> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="document_to_test_formatting.lists_and_tables.lists"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.lists" title="Lists">Lists</a> </h3></div></div></div> <p> A numbered list: </p> <div class="orderedlist"><ol class="orderedlist" type="1"> <li class="listitem"> One </li> <li class="listitem"> Two </li> <li class="listitem"> Three <div class="orderedlist"><ol class="orderedlist" type="a"> <li class="listitem"> Three.a </li> <li class="listitem"> Three.b </li> <li class="listitem"> Three.c </li> </ol></div> </li> <li class="listitem"> Four <div class="orderedlist"><ol class="orderedlist" type="a"><li class="listitem"> Four.a <div class="orderedlist"><ol class="orderedlist" type="i"> <li class="listitem"> Four.a.i </li> <li class="listitem"> Four.a.ii </li> </ol></div> </li></ol></div> </li> <li class="listitem"> Five </li> </ol></div> <p> An unordered list: </p> <div class="itemizedlist"><ul class="itemizedlist" type="disc"> <li class="listitem"> First </li> <li class="listitem"> Second </li> <li class="listitem"> Third </li> </ul></div> <p> A mixture of the two: </p> <div class="orderedlist"><ol class="orderedlist" type="1"> <li class="listitem"> 1 <div class="itemizedlist"><ul class="itemizedlist" type="disc"> <li class="listitem"> 1.a <div class="orderedlist"><ol class="orderedlist" type="a"> <li class="listitem"> 1.a.1 </li> <li class="listitem"> 1.a.2 </li> </ol></div> </li> <li class="listitem"> 1.b </li> </ul></div> </li> <li class="listitem"> 2 <div class="itemizedlist"><ul class="itemizedlist" type="disc"> <li class="listitem"> 2.a </li> <li class="listitem"> 2.b <div class="orderedlist"><ol class="orderedlist" type="a"> <li class="listitem"> 2.b.1 </li> <li class="listitem"> 2.b.2 <div class="itemizedlist"><ul class="itemizedlist" type="circle"> <li class="listitem"> 2.b.2.a </li> <li class="listitem"> 2.b.2.b </li> </ul></div> </li> </ol></div> </li> </ul></div> </li> </ol></div> </div> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="document_to_test_formatting.lists_and_tables.variable_lists"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.variable_lists" title="Variable Lists">Variable Lists</a> </h3></div></div></div> <div class="variablelist"> <p class="title"><b>A Variable List</b></p> <dl> <dt><span class="term">term 1</span></dt> <dd><p> The definition of term 1 </p></dd> <dt><span class="term">term 2</span></dt> <dd><p> The definition of term 2 </p></dd> <dt><span class="term">term 3</span></dt> <dd><p> The definition of term 3 </p></dd> </dl> </div> </div> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="document_to_test_formatting.lists_and_tables.tables"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.tables" title="Tables">Tables</a> </h3></div></div></div> <p> Here's a big table with code and other tricky things: </p> <div class="table"> <a name="id769721"></a><p class="title"><b>Table 1. Notes on the Implementation of the Beta Distribution</b></p> <div class="table-contents"><table class="table" summary="Notes on the Implementation of the Beta Distribution"> <colgroup> <col> <col> </colgroup> <thead><tr> <th> <p> Function </p> </th> <th> <p> Implementation Notes </p> </th> </tr></thead> <tbody> <tr> <td> <p> pdf </p> </td> <td> <p> f(x;α,β) = x<sup>α - 1</sup> (1 - x)<sup>β -1</sup> / B(α, β) </p> <p> Implemented using ibeta_derivative(a, b, x). </p> </td> </tr> <tr> <td> <p> cdf </p> </td> <td> <p> Using the incomplete beta function ibeta(a, b, x) </p> </td> </tr> <tr> <td> <p> cdf complement </p> </td> <td> <p> ibetac(a, b, x) </p> </td> </tr> <tr> <td> <p> quantile </p> </td> <td> <p> Using the inverse incomplete beta function ibeta_inv(a, b, p) </p> </td> </tr> <tr> <td> <p> quantile from the complement </p> </td> <td> <p> ibetac_inv(a, b, q) </p> </td> </tr> <tr> <td> <p> mean </p> </td> <td> <p> <code class="computeroutput"><span class="identifier">a</span><span class="special">/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> variance </p> </td> <td> <p> <code class="computeroutput"><span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)^</span><span class="number">2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> mode </p> </td> <td> <p> <code class="computeroutput"><span class="special">(</span><span class="identifier">a</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span> <span class="special">+</span> <span class="number">2</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> skewness </p> </td> <td> <p> <code class="computeroutput"><span class="number">2</span> <span class="special">(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> kurtosis excess </p> </td> <td> <p> <span class="inlinemediaobject"><img src="../images/beta_dist_kurtosis.png" alt="beta_dist_kurtosis"></span> </p> </td> </tr> <tr> <td> <p> kurtosis </p> </td> <td> <p> <code class="computeroutput"><span class="identifier">kurtosis</span> <span class="special">+</span> <span class="number">3</span></code> </p> </td> </tr> <tr> <td> <p> parameter estimation </p> </td> <td> </td> </tr> <tr> <td> <p> alpha </p> <p> from mean and variance </p> </td> <td> <p> <code class="computeroutput"><span class="identifier">mean</span> <span class="special">*</span> <span class="special">((</span> <span class="special">(</span><span class="identifier">mean</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">variance</span><span class="special">)-</span> <span class="number">1</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> beta </p> <p> from mean and variance </p> </td> <td> <p> <code class="computeroutput"><span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">*</span> <span class="special">(((</span><span class="identifier">mean</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span><span class="identifier">variance</span><span class="special">)-</span><span class="number">1</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> The member functions <code class="computeroutput"><span class="identifier">estimate_alpha</span></code> and <code class="computeroutput"><span class="identifier">estimate_beta</span></code> </p> <p> from cdf and probability x </p> <p> and <span class="bold"><strong>either</strong></span> <code class="computeroutput"><span class="identifier">alpha</span></code> or <code class="computeroutput"><span class="identifier">beta</span></code> </p> </td> <td> <p> Implemented in terms of the inverse incomplete beta functions </p> <p> ibeta_inva, and ibeta_invb respectively. </p> </td> </tr> <tr> <td> <p> <code class="computeroutput"><span class="identifier">estimate_alpha</span></code> </p> </td> <td> <p> <code class="computeroutput"><span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">beta</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">)</span></code> </p> </td> </tr> <tr> <td> <p> <code class="computeroutput"><span class="identifier">estimate_beta</span></code> </p> </td> <td> <p> <code class="computeroutput"><span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">)</span></code> </p> </td> </tr> </tbody> </table></div> </div> <br class="table-break"> </div> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2007 John Maddock, Joel de Guzman, Eric Niebler and Matias Capeletto<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="blurbs.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="images.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>